Problem: Simplify; express your answer in exponential form. Assume $q\neq 0, t\neq 0$. $\dfrac{{(q)^{2}}}{{(q^{2}t^{-2})^{2}}}$
To start, try working on the numerator and the denominator independently. In the numerator, we have ${q}$ to the exponent ${2}$ . Now ${1 \times 2 = 2}$ , so ${(q)^{2} = q^{2}}$ In the denominator, we can use the distributive property of exponents. ${(q^{2}t^{-2})^{2} = (q^{2})^{2}(t^{-2})^{2}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(q)^{2}}}{{(q^{2}t^{-2})^{2}}} = \dfrac{{q^{2}}}{{q^{4}t^{-4}}}$ Break up the equation by variable and simplify. $\dfrac{{q^{2}}}{{q^{4}t^{-4}}} = \dfrac{{q^{2}}}{{q^{4}}} \cdot \dfrac{{1}}{{t^{-4}}} = q^{{2} - {4}} \cdot t^{- {(-4)}} = q^{-2}t^{4}$.